Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii

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              <pb o="77" file="0091" n="91" rhead="SECTIO QUARTA."/>
            quiritur, ut in æquatione ultimâ paragraphi decimi ſexti ponatur {nne/mm} pro
              <lb/>
            v, ſic autem erit
              <lb/>
            {nne/mm} = {nn(a - z)/mm} - {nna/mm}:</s>
            <s xml:id="echoid-s2106" xml:space="preserve">c{mz/nb}√{g/n}
              <lb/>
            hincque deducitur {mz/nb}√{g/n} = log.</s>
            <s xml:id="echoid-s2107" xml:space="preserve">{a/a - e - z}; </s>
            <s xml:id="echoid-s2108" xml:space="preserve">hic vero cum e ponatur defice-
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            re notabiliter ab a poteſt rejici littera z ſigno logarithmicali involuta, unde
              <lb/>
            obtinetur
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            z = {nb/m}√{n/g} X log.</s>
            <s xml:id="echoid-s2109" xml:space="preserve">{a/a - e}</s>
          </p>
          <p>
            <s xml:id="echoid-s2110" xml:space="preserve">Hæc vero æquatio jam indicat ſpatiolum, quod eſt infinite parvum,
              <lb/>
            & </s>
            <s xml:id="echoid-s2111" xml:space="preserve">per quod deſcendit ſuperficies aquæ, dum à quiete velocitas aquæ effluen-
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            tis tanta ſit, quæ debeatur altitudini e; </s>
            <s xml:id="echoid-s2112" xml:space="preserve">ſeque habet hoc ſpatiolum ad illud pa-
              <lb/>
            ragrapho decimo ſeptimo indicatum, quo nempe velocitas maxima oritur, ut
              <lb/>
            log. </s>
            <s xml:id="echoid-s2113" xml:space="preserve">{a/a - e} ad log. </s>
            <s xml:id="echoid-s2114" xml:space="preserve">({ma/nb}√{g/n}) ita ut primum ſit infinities minus altero, etſi
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            pariter infinite parvo.</s>
            <s xml:id="echoid-s2115" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2116" xml:space="preserve">Si porro definita quantitas z multiplicetur per m, obtinetur quantitas
              <lb/>
            aquæ effluentis dum illa velocitas altitudini e debita producitur, quæ proin
              <lb/>
            quantitas eſt æqualis
              <lb/>
            nb√{n/g} X log.</s>
            <s xml:id="echoid-s2117" xml:space="preserve">{a@/a - e}
              <lb/>
            atque ſic finitæ magnitudinis, & </s>
            <s xml:id="echoid-s2118" xml:space="preserve">quidem eo majoris, quo longior ſumitur tu-
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            bus, & </s>
            <s xml:id="echoid-s2119" xml:space="preserve">quo major jactus expectatur.</s>
            <s xml:id="echoid-s2120" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2121" xml:space="preserve">Denique tempus, quo idem fit, ſi recte ſeligantur termini rejiciendi,
              <lb/>
            reperitur æquale
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            2√({nbb/ag} log.</s>
            <s xml:id="echoid-s2122" xml:space="preserve">{a/a - e})
              <lb/>
            atque ſic finitum ſed admodum parvum & </s>
            <s xml:id="echoid-s2123" xml:space="preserve">in nullo exemplo ultra minutum ſe-
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            cundum facile extendendum.</s>
            <s xml:id="echoid-s2124" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2125" xml:space="preserve">§. </s>
            <s xml:id="echoid-s2126" xml:space="preserve">21. </s>
            <s xml:id="echoid-s2127" xml:space="preserve">Hæc omnia accurate examinare ac proſequi volui, tum quod
              <lb/>
            multorum phænomenorum, quæ in effluxu aquarum obſervari ſolent, ſolu-
              <lb/>
            tio inde pendeat, tum etiam ut illas mutationes, quæ ſenſibus plane ſunt im-
              <lb/>
            perceptibiles, animo recte aſſequeremur. </s>
            <s xml:id="echoid-s2128" xml:space="preserve">Multi fuerunt, qui tranſitus ab </s>
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